intermolecular attractions that must be spatially rearranged between sliding a tube (a
flagellum, say) lengthwise versus sideways through water. For reasons that may or
may not be intuitively obvious (depending upon your brain wiring), the difference is
∼1.7-fold. So, a cilium can be pushed backward perpendicular to the direction of
motion, and then pulled back forward with most of the motion parallel to the
trajectory (Fig. 1.3).
Fig. 1.3 Successive positions in the power and recovery strokes of a cilium.
(^) In the return stroke, the cilium’s flexibility completes the motion as a rolling curl
along the length. The viscous drag differential shoves the cell ahead. An alternate
mode of exploiting the difference between along-shaft and across-shaft drag is use of
flagellae wound into spirals. When rotated relative to the cell, often by molecular-
scale rotary “motors”, the vector component of the motion that is perpendicular to the
axis of the spiral is sufficient to drive the cell steadily forward. There are many
features of swimming (or filter feeding for that matter) in the viscous mode that are
unexpected based on our experiences of swimming. When dominant, viscous drag is
sufficiently powerful that there are no eddies shed aft or to the side. There is no
inertial “carry” comparable to the long forward drift you experience after a swimming
stroke. Rather, when force is not being exerted, there is remarkably close to zero
continued forward motion; the stop is effectively instantaneous.
(^) These two modes of swimming appear to be similar in some respects. Both ciliary
motion and propulsion by lateral fins involve pushing back with a high drag element,
then sliding it back forward by feathering or switching angles. The sources of the
effective drag force, however, are substantially different. Some plankton, most
particularly copepods, exploit the interface between drag dominated by inertia and
drag dominated by viscosity. Because they are of intermediate size, with l = 0.1 to
∼1.0 cm, they can accelerate to sufficient v to enter the realm of inertial swimming
(raising the Re), using paddle-like feet and tail-fan sweeps to accelerate to achieve